hhb83 发表于 2009-12-6 13:03 
谢谢！那请问多人非零和是什么样子呢，从上面的式子中我推不太出来啊，谢谢！
For non-0-sum games: you probably need Mixed Integer Programs.
for 2-player non-0-sum game:
for player 1 (pay-off: a[i,j]):
x
: mixed strat
s: 0-1 varialbe, 1 if strat i is usable.
v: expected pay-off of strat i
maxv:= max_i v
for player 2 (pay-off b[i,j]):
y[j]: mixed start
t[j]: 0-1 variable, 1 if strat j is usable
w[j]: expected pay=off of strat j
maxw:=max_j w[j]
Max maxv + maxw
ST:
sum x =1
sum y[j] = 1
v = sum a[i,j] y[j], forall i
w[j] = sum b[i,j] x, forall j
...
M (1 - s) >= maxv - v //big-M method
0 <= x <= s //x must be zero if s = 0
M ( 1 - t[j] ) >= maxw - w[j]
0 <= w[j] <= t[t]
扫码加好友，拉您进群
全部版块
我的主页
收藏
